Tensors | Tensors in general relativity

Bach tensor

In differential geometry and general relativity, the Bach tensor is a trace-free tensor of rank 2 which is conformally invariant in dimension n = 4. Before 1968, it was the only known conformally invariant tensor that is algebraically independent of the Weyl tensor. In abstract indices the Bach tensor is given by where is the Weyl tensor, and the Schouten tensor given in terms of the Ricci tensor and scalar curvature by (Wikipedia).

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Related pages

Weyl tensor | Schouten tensor | Tensor | Differential geometry | Cotton tensor | Abstract index notation | Scalar curvature